{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OFF2FLQ5KXJWV3U6L6WYKSJ46A","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e2d49cfe789f74983f75f83dbc5d1223a6b8350387fe8e7b93a914339c63e633","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-14T22:13:01Z","title_canon_sha256":"0b2eab8f66dff74fa44174ef89129c0a0ef0b9d70ea44c3f607a1410bb9e7ebc"},"schema_version":"1.0","source":{"id":"0910.2737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2737","created_at":"2026-07-04T15:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2737v1","created_at":"2026-07-04T15:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2737","created_at":"2026-07-04T15:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"OFF2FLQ5KXJW","created_at":"2026-07-04T15:54:30Z"},{"alias_kind":"pith_short_16","alias_value":"OFF2FLQ5KXJWV3U6","created_at":"2026-07-04T15:54:30Z"},{"alias_kind":"pith_short_8","alias_value":"OFF2FLQ5","created_at":"2026-07-04T15:54:30Z"}],"graph_snapshots":[{"event_id":"sha256:6978249cb8f03c1441dbbcd0dca98b7ca366f1836453726f0b51a9065f273579","target":"graph","created_at":"2026-07-04T15:54:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0910.2737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics: Knot Theory, Categorical Quantum Mechanics, and Logic and Computation.\n  We shall focus in particular on the following two topics:\n  - The Temperley-Lieb algebra has always hitherto been presented as a quotient of some sort: either algebraically by generators and relations as in Jones' original presentation, or as a diagram algebra modulo planar isotopy as in Kauffman's presentation. We shall use tools from Geometry of Interaction, a ","authors_text":"Samson Abramsky","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-14T22:13:01Z","title":"Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2737","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:12d51968ffc4320e82b7dab901ab0d4592ef6a5f6e5b9fa0a641bd70a0993c0d","target":"record","created_at":"2026-07-04T15:54:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e2d49cfe789f74983f75f83dbc5d1223a6b8350387fe8e7b93a914339c63e633","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-14T22:13:01Z","title_canon_sha256":"0b2eab8f66dff74fa44174ef89129c0a0ef0b9d70ea44c3f607a1410bb9e7ebc"},"schema_version":"1.0","source":{"id":"0910.2737","kind":"arxiv","version":1}},"canonical_sha256":"714ba2ae1d55d36aee9e5fad85493cf0209344911bfe81df4cd03e74a39a4018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"714ba2ae1d55d36aee9e5fad85493cf0209344911bfe81df4cd03e74a39a4018","first_computed_at":"2026-07-04T15:54:30.053107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:54:30.053107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G6wpMgfoA4E7FhzW4TPlV5DaLtRGLUuALk5fvHUdh6U7MNwbt3YbRIXM/X+9GTI1FsuIqBumcprNDFKMgAFcCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:54:30.053515Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d51968ffc4320e82b7dab901ab0d4592ef6a5f6e5b9fa0a641bd70a0993c0d","sha256:6978249cb8f03c1441dbbcd0dca98b7ca366f1836453726f0b51a9065f273579"],"state_sha256":"4ce9daa853e4d9c018ca591aa0084f70bb58497339c61905394ee86063089177"}